Comprehensive Guide to Statistical Tests in Biology and Data Analysis

Chi-Squared Test

Compares observed vs expected frequencies for one categorical variable.

When to use Chi-Squared Test?

When comparing one categorical variable's observed counts to expected counts.

Example of Chi-Squared Test

Testing if 100 bees choose yellow, blue, or red discs equally.

Chi-Squared Contingency Table Test

Compares two or more categorical variables to see if they are associated.

When to use Chi-Squared Contingency Table?

When testing if two categorical variables (like gender and strategy) are related.

Shapiro Test

Tests whether a dataset follows a normal distribution.

When to use Shapiro Test?

Before parametric tests to confirm normality.

Two-Tailed T-test

Compares a sample mean to a fixed/hypothetical value.

Example of Two-Tailed T-test

Testing if plant isotope concentration equals the known air concentration.

One-Sided T-test

Tests whether a sample mean is greater than OR less than a fixed value.

Example of One-Sided T-test

Testing if a drug lowers body temperature below 102°F.

Two-Sample T-test

Compares means of two independent groups.

Example of Two-Sample T-test

Comparing anther length in diploid vs tetraploid plants.

Bartlett's Test

Tests if variances in two or more groups are equal.

When to use Bartlett's Test?

Before ANOVA; tests homogeneity of variances.

One-Way ANOVA

Compares means across 2+ groups within one categorical variable.

Example of One-Way ANOVA

Testing effect of soil type on plant height.

Two-Way ANOVA

Compares means across 2+ groups in two categorical variables.

Example of Two-Way ANOVA

Testing effects of water level and nitrogen on plant growth.

Mann-Whitney U Test

Nonparametric alternative to two-sample t-test; compares ranked values.

Example of Mann-Whitney

Comparing health scores (1-5) between two cultivars.

Wilcoxon Test

Nonparametric paired t-test; compares ranked paired samples.

Example of Wilcoxon

Comparing rankings from two expert groups on the same farms.

Kruskal-Wallis Test

Nonparametric ANOVA; compares ranked medians of 3+ groups.

Example of Kruskal-Wallis

Used when 3+ non-normal groups need comparison.

Friedman Test

Nonparametric two-way ANOVA for ranked repeated measures.

Example of Friedman Test

Comparing allergic response severity across 3 pollen species.

Tukey HSD Test

Post-hoc test used after a significant ANOVA to find which groups differ.

AIC Test

Model selection test; lower AIC = better model.

Correlation

Measures relationship between two quantitative variables without causation.

Simple Linear Regression

Examines impact of ONE predictor on ONE response variable.

Multiple Regression

Examines impact of 2+ quantitative predictors on a quantitative response.

General Linear Model (GLM)

Handles continuous/categorical predictors to predict a continuous response.

Generalized Linear Model (GzLM)

Used when the outcome follows binomial, Poisson, or gamma distribution.

Polynomial Regression

Models curved (non-linear but polynomial) relationships.

Nonlinear Regression

Models complex relationships that are not linear or polynomial.

What test compares plant height across four soil types?

One-Way ANOVA.

After ANOVA shows significance, what test tells which groups differ?

Tukey HSD.

What test checks if data are normally distributed?

Shapiro Test.

What test compares average body mass of two frog species?

Two-Sample T-test (or Mann-Whitney if not normal).

What test compares hormone levels before & after a storm?

Paired T-test (or Wilcoxon if not normal).

What test compares nesting material preference between male & female birds?

Chi-Squared Contingency Table.

What test checks if bees choose flower colors randomly?

Chi-Squared Goodness of Fit.

What test compares 2 factors (like water × sunlight) on plant height?

TAB Two-Way ANOVA.

What test predicts leaf litter from tree density?

Simple Linear Regression.

What test predicts crop yield from soil nitrogen + rainfall?

Multiple Regression.

What test compares 3 expert evaluators ranking the same items?

Friedman Test.

What test compares health score (1-5) between two cultivars?

Mann-Whitney U Test.

What model predicts survival (yes/no) from seed weight?

Generalized Linear Model (binomial).

How do you choose the best model?

Lowest AIC value.

What test is used for curved relationships like enzyme kinetics?

Nonlinear Regression.

What test compares skewed data from 3+ groups?

Kruskal-Wallis.

What test checks one-direction changes (increase or decrease only)?

One-Sided T-test.

What test compares variances across three diet groups?

Bartlett's Test.

What does p = 0.03 in a t-test mean?

Reject H0; means are significantly different.

What does p > 0.05 in a chi-square test mean?

Observed matches expected; no association.

ANOVA p < 0.01 means what?

At least one group mean differs; need post-hoc test.

Mann-Whitney p < 0.05 means what?

The group medians/distributions differ.

Regression R² = 0.70 means what?

Predictors explain 70% of response variation.

Shapiro p = 0.001 means what?

Data are not normal; use nonparametric tests.

GLM (binomial) with positive coefficient means what?

Probability of response increases with predictor.

Model AIC 112 vs AIC 129 — which is better?

AIC 112; lowest AIC = best.

What does a significant interaction in Two-Way ANOVA mean?

One factor's effect depends on the other factor.

Correlation r = -0.8 means what?

Strong negative relationship between variables.

Which tests use ranked data?

Mann-Whitney, Wilcoxon, Kruskal-Wallis, Friedman.

Requirements for ANOVA?

Normal data + equal variances.

What test compares paired data?

Paired T-test or Wilcoxon.

What does chi-square measure?

Difference between observed and expected counts.

Why doesn't correlation imply causation?

No defined explanatory or response variable.

Main purpose of regression?

Predict or explain a response variable.

What makes a regression "generalized"?

Uses non-normal error distributions (binomial, Poisson).